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On the continuation for variational inequalities depending on an eigenvalue parameter

In this paper we generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.     

On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

Multicyclic polyethers derived from 1,1,1‐tris(4‐hydroxyphenyl)ethane and 2,6‐dihalopyridines

Poly(pyridine ether)s were prepared in two ways: the polycondensation of silylated 1,1,1‐tris(4‐hydroxyphenyl)ethane (THPE) with 2,6‐difluoropyridine (method A) and the polycondensation of free THPE with 2,6‐dichloropyridine (method B). With method A, the THPE/difluoropyridine feed ratio was varied from 1.0:1.0 to 1.0:1.6. Cycles, bicycles, and multicycles were the main reaction products, and crosslinking was never observed. When ideal stoichiometry was used exclusively, multicycles free of functional groups were obtained. These multicycles were detectable in matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectra up to B₃₈C₇₆ with a mass of approximately 32,000 Da. With method B, the reaction conditions were varied at a fixed feed ratio to achieve an optimum for the preparation of multicyclic polyethers, but because of the lower reactivity of 2,6‐dichloropyridine, a quantitative conversion was not achieved. The reaction products were characterized with MALDI‐TOF mass spectrometry, viscosity measurements, and size exclusion chromatography. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5725–5735, 2004     

Differential scanning calorimetry and thermogravimetric analysis investigation of the thermal properties and degradation of some radiation‐grafted films and membranes

The influence of irradiation and grafting on the crystallinity of three base polymers has been investigated with differential scanning calorimetry. Grafting has the largest effect on the base polymer crystallinity and results in a reduction of the crystallinity. The thermal degradation of the base polymers and grafted films has been investigated with thermogravimetric analysis. The extent of the fluorination of the base polymer, the irradiation method, and the graft level all influence the thermal degradation and its activation energy. It is proposed that the variation of the chain lengths of the grafted polystyrene chains is actually a primary underlying factor responsible for the influence of these various parameters on the degradation process. The first results of a comparative thermal analysis of some fuel‐cell membranes are also presented, and the promise and shortcomings of this method are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2612–2624, 2004     

Matrix extensions and eigenvalue completions, the generic case

In this paper we provide new necessary and sufficient conditions for the so-called eigenvalue completion problem.